Control system

ABSTRACT

A control system that constantly and accurately controls a control variable so that it remains within an allowable range is provided. The control system in accordance with the present invention estimates a steady-state deviation d in a controlled object as a steady-state deviation estimation value d′ on the basis of a control variable y and a final desired value y 2 . A control variable y in a controlled object based on the initial desired value y 1  is estimated as the primary estimation value y 1 ′ on the basis of at least the initial desired value y 1  and the steady-state deviation estimation value d′. If a primary estimation value y 1 ′ is within an allowable range, then a final desired value y 2  agreeing with an initial desired value y 1  is determined, while, if the primary estimation value y 1 ′ is out of the allowable range, then the final desired value y 2  is determined on the basis of at least a boundary value of the allowable range. A manipulation variable x is determined on the basis of the final desired value y 2 .

TECHNICAL FIELD

The present invention relates to a system for controlling a controlvariable of a controlled object.

BACKGROUND ART

Hitherto, as a control system having a limiting function, a controlsystem A shown in FIG. 12 has been known. An output (control variable) yof a controlled object B is controlled by the control system A.

The control system A is equipped with a manipulation variabledetermining unit A₁, a limiter A₂, and an integrating unit A₃.

The manipulation variable determining unit A₁ has a transmission elementG₀ and outputs a primary manipulation variable x₁ according to anexpression (a) shown below on the basis of a difference y₀−y between adesired value y₀ and the control variable y.x ₁ =G ₀·(y ₀ −y)  (a)

The limiter A₂ outputs a secondary manipulation variable x₂ on the basisof an input of the primary manipulation variable x₁. To be morespecific, the limiter A₂ directly outputs the primary manipulationvariable x₁ as the secondary manipulation variable x₂ if the primarymanipulation variable x₁ remains in a predetermined range. If, on theother hand, the primary manipulation variable x₁ is out of thepredetermined range, then the limiter A₂ outputs a boundary value of therange as the secondary manipulation variable x₂.

The integrating unit A₃ has an integrating element K/s and outputs afinal manipulation variable x according to an expression (b) given belowon the basis of an input of a difference between the second manipulationvariable x₂ and the control variable y.x=(K/s)·(x ₂ −y)  (b)

The controlled object B has a transmission element G and outputs thecontrol variable y according to an expression (c) given below on thebasis of an input of the manipulation variable x.y=G·x+d  (c)

-   -   where “d” denotes a steady-state deviation (offset) in the        controlled object B.

According to the control system A having the aforesaid construction, ifthe control variable y is likely to be out of an “allowable range” basedon the primary manipulation variable x₁, then the secondary manipulationvariable x₂ is determined such that the primary manipulation variable x₁is limited to be within the predetermined range by the limiter A₂. Thus,the control is conducted so as to restrict the control variable y to bewithin the allowable range.

A feedback loop comprised of the integrating unit A₃ and an adder A₄located immediately upstream relative to the integrating unit A₃determines the control variable x such that the steady-state deviation dof the controlled object B is cancelled. This allows control to becarried out such that the control variable y remains in the allowablerange even if there is the steady-state deviation d.

If, however, a gain coefficient K (refer to expression (b)) in theintegrating unit A₃ is high, then the feedback loop becomes unstable andoscillates or vibrates; therefore, the gain coefficient K must becontrolled low. Thus, the responsiveness of the control variable youtput from the controlled object B relative to the desired value y₀input to the control system A undesirably deteriorates. As a result, anerror (inaccuracy) of the control variable y relative to the desiredvalue y₀ increases, and control accuracy may deteriorate and the controlvariable y may be out of the allowable range.

Accordingly, the present invention is intended to provide, as asolution, a control system that permits stable and accurate control soas to maintain a control variable in an allowable range.

DISCLOSURE OF INVENTION

The present invention relates to a control system for controlling acontrol variable y of a controlled object by a manipulation variable x.

A control system in accordance with the present invention as a solutionto the aforesaid problem includes a steady-state deviation estimatingmeans for estimating a steady-state deviation d in a controlled objectas a steady-state deviation estimation value d′ on the basis of thecontrol variable y and a final desired value y₂, a primary estimatingmeans for estimating the control variable y of the controlled objectaccording to an initial desired value y₁ as a primary estimation valuey₁′ on the basis of at least the initial desired value y₁ and thesteady-state deviation estimation value d′, a desired value determiningmeans for determining the final desired value y₂ agreeing with theinitial desired value y₁ if the primary estimation value y₁′ is withinan allowable range, while determining the final desired value y₂ basedon at least a boundary value of the allowable range if the primaryestimation value y₁′ is out of the allowable range, and a manipulationvariable determining means for determining a manipulation variable xaccording to the final desired value y₂.

According to the present invention, if the primary estimation value y₁′(=estimation value of control variable y with the steady-state deviationd taken into account) is within the allowable range, then the finaldesired value y₂ that agrees (or substantially agrees) with the initialdesired value y₁ is determined. In other words, the transmission element(a transmission element of the desired value determining means beingalso included) may be regarded as “1” from the initial desired value y₁to the final desired value y₂ in a control system. Furthermore, themanipulation variable x is determined on the basis of the final desiredvalue y₂, and then the control variable y is controlled on the basis ofthe manipulation variable x.

The initial desired value y₁ is determined as it is as the final desiredvalue y₂ and the manipulation variable x is further determined, so thatphase lags of the manipulation variable x and the control variable yrelative to the initial desired value y₁ can be markedly reduced.

If the primary estimation value y₁′ is out of the allowable range, thenthe final desired value y₂ is determined on the basis of the “boundaryvalue” of the allowable range. This makes it possible to conduct controlso as to maintain the control variable y to remain in the allowablerange even if there is the steady-state deviation d.

Hence, according to the present invention, a secondary estimation valuey₂′ is determined, taking the steady-state deviation d into account, soas to remain within the allowable range, and the phase lag of thecontrol variable y relative to the initial desired value y₁ isrestrained. With this arrangement, stable and accurate control can beaccomplished to prevent the control variable y from being out of theallowable range.

The control variable y may be one-dimensional (scalar) ormultiple-dimensional (vector).

The present invention is characterized in that the steady-statedeviation estimating means estimates, as the steady-state deviationestimation value d′, the difference between the control variable y and avalue obtained by passing the final desired value y₂ through a low-passfilter or a delaying means.

Furthermore, the present invention is characterized in that thesteady-state deviation estimating means estimates, as the steady-statedeviation estimation value d′, the difference between a value obtainedby passing the control variable y through the low-pass filter or thedelaying means and a value obtained by passing the final desired valuey₂ through the low-pass filter or the delaying means.

Furthermore, the present invention is characterized in that thesteady-state deviation estimating means estimates, as the steady-statedeviation estimation value d′, a value obtained by passing thedifference between the control variable y and the final desired value y₂through a low-pass filter or a delaying means.

According to the present invention, the oscillation of the steady-statedeviation estimation value d′ is restrained by the low-pass filter orthe delaying means, allowing the steady-state deviation estimation valued′ to be accurately estimated. The final desired value y₂ is determinedaccording to whether the primary estimation value y₁′ based on thesteady-state deviation estimation value d′ is within the allowablerange, and then the control variable y is controlled. Thus, the controlvariable y can be stably controlled so as not to be out of the allowablerange regardless of the presence of the steady-state deviation d.

The “delaying means” refers to a means for saving a previous value andoutputting it for the next time (the present time) in a digital circuit.

Furthermore, the present invention is characterized in that the primaryestimating means estimates a sum of the initial desired value y₁ and thesteady-state deviation estimation value d′ or a value obtained bypassing the sum y₁+d′ through the low-pass filter or the delaying meansas the primary estimation value y₁′.

According to the present invention, the primary estimation value y₁′ canbe accurately determined on the basis of the initial desired value y₁and the steady-state deviation estimation value d′. This allows thecontrol variable y to be stably controlled so as not to be out of theallowable range.

The present invention is characterized by being provided with asecondary estimating means for directly using the primary estimationvalue y₁′ as the secondary estimation value y₂′ if the primaryestimation value y₁′ is within the allowable range, while using a valuewithin the allowable range as the secondary estimation value y₂′ if theprimary estimation value y₁′ is out of the allowable range, and thedesired value determining means determines the final desired value y₂ onthe basis of the secondary estimation value y₂′ and the steady-statedeviation estimation value d′.

Furthermore, the present invention is characterized in that, based onthe primary estimation value y₁′ the secondary estimating meansdetermines the secondary estimation value y₂′ by continuous or smoothmapping from the primary estimation value y₁′ to the secondaryestimation value y₂′.

According to the present invention, the secondary estimation value y₂′is determined on the basis of the continuous or smooth mapping, allowingthe control variable y to be continuously or smoothly controlled.

Mapping f being “continuous” means that, when a distance (distance norm)between point a and point b is converged to zero, the distance betweenmappings f (a) and f (b) is also converted to zero, while mapping f (p)is continuous if a variable p is continuous. The mapping f being“smooth” means that grad (gradient) of the mapping f is continuous.

The present invention is characterized in that the desired valuedetermining means subtracts the steady-state deviation estimation valued′ from the secondary estimation value y₂′ to determine the finaldesired value y₂.

The present invention is characterized in that the desired valuedetermining means determines the final desired value y₂ on the basis ofa difference between the control variable y and the secondary estimationvalue y₂′ or a difference between the secondary estimation value y₂′ anda value obtained by passing the control variable y through a low-passfilter or a delaying means according to a control rule for convergingthe difference to zero.

The present invention is characterized in that the desired valuedetermining means determines the final desired value y₂ by passing adifference between the control variable y and the secondary estimationvalue y₂′ or a difference between a value obtained by passing thecontrol variable y through a filter or a delaying means and thesecondary estimation value y₂′ through a transmission element having atleast integration.

According to the present invention, if the primary estimation value y₁′corresponds to a sum of the initial desired value y₁ and thesteady-state deviation estimation value d′ or if it corresponds to thesum and also remains in the allowable range, then the final desiredvalue y₂ agreeing (or substantially agreeing) with the initial desiredvalue y₁ can be determined. This allows the control variable y to bestably and accurately controlled so as to stay within the allowablerange regardless of the presence or the absence of the steady-statedeviation d.

Furthermore, the present invention is characterized in that themanipulation variable determining means has a transmission function Gm⁻¹that satisfies a relationship of Gm⁻¹·G≈1 between itself and thetransmission function G of a controlled object.

According to the present invention, even if there is a phase lag of thecontrol variable y relative to the manipulation variable x in acontrolled object, the phase lag can be compensated. Hence, the controlvariable y can be accurately and stably controlled on the basis of themanipulation variable x according to the final desired value y₂.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a control system according to a firstembodiment of the present invention,

FIG. 2 is a block diagram of a control system according to a secondembodiment of the present invention,

FIG. 3 is a block diagram of a control system according to a thirdembodiment of the present invention,

FIG. 4 is a block diagram of a control system according to a fourthembodiment of the present invention,

FIG. 5 is a block diagram of a control system according to a fifthembodiment of the present invention,

FIG. 6 is a block diagram of a control system according to a sixthembodiment of the present invention,

FIG. 7(a) and FIG. 7(b) are explanatory drawings of an allowable range(one-dimensional),

FIG. 8 is a block diagram of a manipulator, which is a controlled objectin the sixth embodiment,

FIG. 9 is an explanatory drawing of an allowable range(two-dimensional),

FIG. 10 is an explanatory drawing of n-dimensional mapping based on anallowable range (n-dimensional),

FIG. 11 is a block diagram of a control system according to anotherembodiment of the present invention, and

FIG. 12 is a block diagram of a conventional control system.

BEST MODE FOR CARRYING OUT THE INVENTION

Embodiments according to the present invention will be explained inconjunction with the accompanying drawings.

First, a control system according to a first embodiment of the presentinvention will be explained in conjunction with FIG. 1 through FIG. 7.

A control system 100 according to a first embodiment shown in FIG. 1 isequipped with a limiter 111, an inverse model arithmetic unit 112, afirst filter 113, and a second filter 114. The control system 100controls a control variable y of a controlled object 200 on the basis ofa manipulation variable x.

The limiter 111 constitutes a “secondary estimating means” anddetermines and outputs a secondary estimation value y₂′ according to aninput primary estimation value y₁′ on the basis of a mapping function(refer to FIG. 7(a)) represented by an expression (1) given below:y₂′=y₁′ (if y⁻≦y₁′≦y₊)y₊ (if y+<y₁′)y⁻ (if y₁′<y⁻)  (1)

More specifically, if the primary estimation value y₁′ is within anallowable range [y⁻, y₊], then the limiter 111 determines the secondaryestimation value y₂′ that agrees with the primary estimation value y₁′.If the primary estimation value y₁′ exceeds an upper limit value y+ofthe allowable range [y⁻, y₊], then the limiter 111 determines thesecondary estimation value y₂′ agreeing with the upper limit value y+.Furthermore, if the primary estimation value y₁′ is below a lower limitvalue y of the allowable range [y⁻, y₊], then the limiter 111 determinesthe secondary estimation value y₂′ agreeing with the lower limit valuey⁻.

The mapping function representing the characteristic of the limiter 111may be continuous and smooth mapping function of an S-shaped curve orthe like shown in FIG. 7(b). The allowable range [y⁻, y₊] may be setbeforehand to make it easy to set a mapping function that has saturationcharacteristics. Alternatively, the allowable range [y⁻, y₊] may besequentially changed according to conditions.

The inverse model arithmetic unit 112 constituting a “manipulationvariable determining means” has a transmission element Gm⁻¹ having arelationship represented by an expression (2) given below between itselfand a transmission element G of the controlled object 200, and outputsthe manipulation variable x according to an expression (3) given belowon the basis of an input of final desired value y₂.Gm ⁻¹ ·G≈1  (2)x=Gm ⁻¹ ·y ₂  (3)

The first filter 113 and the second filter 114 constitute a“steady-state deviation estimating means”. The first filter 113 is afirst-order lag filter of a time constant T₁ and receives the finaldesired value y₂ The second filter 114 is a first-order lag filter of atime constant T₂ and receives the control variable y. Based on outputsof the first filter 113 and the second filter 114, the steady-statedeviation estimation value d′ is determined according to an expression(4) given below.d′=y·{1/(T ₂ s+1)}−y ₂·{1/(T ₁ s+1)}  (4)

The primary estimation value y₁′ is determined according to anexpression (5) given below on the basis of the initial desired value y₁and the steady-state deviation estimation value d′, and the determinedvalue y₁′ is supplied to the limiter 111.y ₁ ′=y ₁ +d′  (5)

Furthermore, the final desired value y₂ is determined according to anexpression (6) given below on the basis of the secondary estimationvalue y₂′ and the steady-state deviation estimation value d′, and thedetermined value y₂ is supplied to the inverse model arithmetic unit112.y ₂ =y ₂ ′−d′  (6)

Considering a phase lag of a series system taking place between theinverse model arithmetic unit 112 and the controlled object 200, thetime constant T₁ of the primary filter 113 and the time constant T₂ ofthe secondary filter 114 are set to be sufficiently large to securestability of the controlled object 200 when the primary estimation valuey₁′ is out of the allowable range [y⁻, y₊]. At the same time, the timeconstants T₁ and T₂ are set to be sufficiently small so as to restraindeterioration of the responsiveness of the controlled object 200 whenthe primary estimation value y₁′ is out of the allowable range [y⁻, y₊].

The controlled object 200 has the transmission element G and outputs thecontrol variable y on the basis of the manipulation variable x accordingto an expression (7) given below.y=G·x+d  (7)

-   -   where d denotes a steady-state deviation (offset) of the        controlled object 200.

According to the control system 100 having the aforesaid construction,“the initial desired value y₁” and the “steady-state deviationestimation value d′” are added up (refer to expression (5)) and the sumof the two values (=y₁+d′) is supplied as “the primary estimation valuey₁′” to the limiter 111. Based on the sum, “the secondary estimationvalue y₂′” is determined according to expression (1) and output by thelimiter 111.

“The steady-state deviation estimation value d′” is based on theimmediately preceding steady-state deviation d and corresponds to thesteady-state deviation d of the controlled object 200 presumed toimmediately follow.

“The primary estimation value y₁′” corresponds to the control variable yestimated by taking the steady-state deviation d into account if themanipulation variable x is determined such that it agrees with theinitial desired value y₁.

“The secondary estimation value y₂′” corresponds to the control variabley estimated by taking the steady-state deviation d into account if thefinal desired value y₂ is determined such that the control variable yremains in the allowable range [y⁻, y₊] and that the manipulationvariable x agrees with the final desired value y₂, in addition to thesteady-state deviation d.

“The steady-state deviation estimation value d′” is subtracted from “thesecondary estimation value y₂′” (refer to expression (6)), and thedifference of the two values (=y₂′−d′) is supplied as “the final desiredvalue y₂” to the inverse model arithmetic unit 112. Thus, “themanipulation variable x (=Gm⁻¹·y₂)” is output according to expression(2) by the inverse model arithmetic unit 112.

Taking the steady-state deviation d into account, the final desiredvalue y₂′ is determined such that the control variable y remains in theallowable range [y⁻, y₊]. “The manipulation variable x” is determined onthe basis of the final desired value y₂.

Furthermore, based on an output of the first filter 113 according to thefinal desired value y₂ and an output of the second filter 114 accordingto the control variable y, the steady-state deviation estimation valued′ is determined by expression (4).

As previously described, the sum of “the initial desired value y₁” and“the steady-state deviation estimation value d′” (=y₁+d′) is supplied as“the primary estimation value y₁,” to the limiter 111, and thedifference between “the secondary estimation value y₂′” and “thesteady-state deviation estimation value d′” (=y₂′−d′) output from thelimiter 111 is supplied as “the final desired value y₂” to the inversemodel arithmetic unit 112.

The control system 100 according to the first embodiment determines “theprimary estimation value y₁′” as the sum of the “initial desired valuey₁” and “the steady-state deviation estimation value d′” (=y₁+d′) (referto expression (5)). “The final desired value y₂” is determined as adifference between “the secondary estimation value y₂” and “thesteady-state deviation estimation value d′” (=y₂′−d′) (refer toexpression (6)). Furthermore, if “the primary estimation value y₁′ (=anestimation value of the control variable y, taking the steady-statedeviation d into account)” is within the allowable range [y⁻, y₊], then“the secondary estimation value y₂′” agreeing with “the primaryestimation value y₁′” is determined (refer to expression (1)).

Accordingly, if the primary estimation value y₁′ is within the allowablerange [y⁻, y₊], then the final desired value y₂ agreeing with theinitial desired value y₁ is determined as represented by an expression(8) given below. In other words, the transmission element may beregarded as “1” from the initial desired value y₁ to the final desiredvalue y₂. $\begin{matrix}\begin{matrix}{y_{2} = {y_{2}^{\prime} - d^{\prime}}} \\{= {y_{1}^{\prime} - d^{\prime}}} \\{= {\left( {y_{1} + d^{\prime}} \right) - d^{\prime}}} \\{= y_{1}}\end{matrix} & (8)\end{matrix}$

Furthermore, the manipulation variable x is determined on the basis ofthe final desired value y₂ (refer to expression (3)), and then thecontrol variable y is controlled on the basis of the manipulationvariable x (refer to expression (7)).

The initial desired value y₁ is directly used as the final desired valuey₂ and the manipulation variable x is determined, so that the phase lagsof the manipulation variable x and the control variable y relative tothe initial desired value y₁ can be markedly reduced.

If the primary estimation value y₁′ is out of the allowable range [y⁻,y₊], then the secondary estimation value y₂′ that agrees with the lowerlimit value y or the upper limit value y+of the allowable range [y⁻, y₊]is determined. Thereafter, the secondary estimation value y₂′ and thefinal desired value y₂ are determined. This makes it possible to carryout control so that the control variable y remains in the allowablerange even if there is the steady-state deviation d.

Moreover, the oscillation of the steady-state deviation estimation valued′ is restrained by the first filter 113. This makes it possible toaccurately estimate the steady-state deviation estimation value d′ andthe primary estimation value y₁′. Then, the final desired value y₂ isdetermined according to whether the primary estimation value y₁′ iswithin the allowable range [y⁻, y₊], and then the control variable y iscontrolled. With this arrangement, control is stably carried out so thatthe control variable y does not go out of the allowable range regardlessof the presence of the steady-state deviation d.

To explain the operation in more detail, if the primary estimation valuey₁′ is out of the allowable range [y⁻, y₊], then the secondaryestimation value y₂′ agreeing with the lower limit value y or the upperlimit value y+is used, so that the transmission function from an inputto an output of the limiter 122, excluding a steady-state component, issubstantially “zero” (as long as the input (the primary estimation valuey₁′) is out of the allowable range [y⁻, y₊], then the output (thesecondary estimation value y₂′) remains constant even if the inputvaries). Hence, an expression (9) given below is obtained by determininga relationship among the secondary estimation value y₂′, thesteady-state deviation d and the control variable y by expressions (2)through (7).y=[{T ₁ T ₂ s ²+(T ₁ +T ₂)s+1}/(T ₁ T ₂ s ²+2T ₁ s+1)]y2′+{(T ₁ T ₂ s ²+T ₁ s)/(T ₁ T ₂ s ²+2T ₁ s+1)}d  (9)

In a low frequency range (s to 0), expression (9) can be approximated toan expression (10) given below.y≈y ₂′  (10)

In other words, the control variable y substantially agrees with thesecondary estimation value y₂′ regardless of the steady-state deviationd. Thus, if the primary estimation value y₁′ is out of the allowablerange [y⁻, y₊], then the control variable y substantially agrees withthe lower limit value y⁻ or the upper limit value y₊ independently ofthe steady-state deviation d.

Accordingly, the secondary estimation value y₂′ is determined such thatit remains in the allowable range [y⁻, y₊], taking the steady-statedeviation d into account, and the phase lag of the control variable yrelative to the initial desired value y₁ is restrained. This allows thecontrol variable y to be stably and accurately controlled so as toremain within the allowable range [y⁻, y₊].

Referring now to FIG. 2, a control system according to a secondembodiment of the present invention will be explained.

A block diagram of a control system 100 according to the secondembodiment shown in FIG. 2 is an equivalent modification of the blockdiagram of the control system 100 according to the first embodimentshown in FIG. 1, and can be approximated to T₁ s to 0 in the lowfrequency range. Hence, the block diagram of the control system 100according to the second embodiment can be obtained by going throughapproximate modifications to (primary lead filter of a time constantT₁)*(limiter) before and after (limiter)*(primary lead filter of timeconstant T₁ (transmission element T₁ s+1)).

From the relationship Gm⁻¹·G≦1 of expression (2), the inverse modelarithmetic unit 112 in the control system 100 according to the firstembodiment is omitted, and the transmission element of a controlledobject 200 is set to 1.

The control system 100 according to the second embodiment shown in FIG.2 is equipped with a filter 121, a limiter 122, an integrating unit 123,and the filter 124.

The filter 121 is a primary lead filter of a time constant T₁ andprovides outputs based on the initial desired value y₁.

The limiter 122 shares the same construction as that of the limiter 111in the control system 100 according to the first embodiment.

The integrating unit 123 carries out integral operation (time constantT₁) using a received difference between an output of the limiter 122 andan output of the filter 124 so as to output the final desired value y₂.

The filter 124 has a transmission element {(T₁ s+1)/(T₂ s+1)} andprovides outputs based on the control variable y. The transmissionelement of the filter 124 can be approximated to T₁ s˜T₂ s˜0 in a lowfrequency band, so that the transmission element of the filter 124 willbe approximated to “1” in the following description.

The integrating unit 123 and the filter 124 constitute “a steady-statedeviation estimating means.” In the second embodiment, the steady-statedeviation estimation value d′ is determined according to an expression(11) as a difference between an output of the integrating unit 123 andan output of the filter 124. $\begin{matrix}\begin{matrix}{d^{\prime} = {{\left\{ {\left( {{T_{1}s} + 1} \right)/\left( {{T_{2}s} + 1} \right)} \right\} \cdot y} - y_{2}}} \\{\approx {{1 \cdot y} - y_{2}}}\end{matrix} & (11)\end{matrix}$

The control system 100 according to the second embodiment adds up anoutput of the filter 121 on the basis of the initial desired value y₁(=(T₁ s+1)·y₁) and the steady-state deviation estimation value d′(=y−y₂) and the sum of the two values is supplied as “the primaryestimation value y₁′” to the limiter 122.

An output (≈y) of the filter 124 is subtracted from “the secondaryestimation value y₂′” (refer to expression (1)) output from the limiter122 on the basis of “the primary estimation value y₁′” and thedifference between the two is passed through the integrating unit 123 soas to determine a “final desired value y₂ (=(y₂′−y)·{1/T₁ s})”.

The control system 100 according to the second embodiment determines thefinal desired value y₂ that agrees with the initial desired value y₁according to a relational expression (12) given below if the primaryestimation value y₁′ is within the allowable range [y⁻, y₊]. In otherwords, the transmission element from the initial desired value y₁ to thefinal desired value y₂ can be regarded as “1”. $\begin{matrix}{y_{2} = {\left( {y_{2}^{\prime} - y} \right) \cdot \left\{ {{1/T_{1}}s} \right\}}} & (12) \\{\quad{= {\left( {y_{1}^{\prime} - y} \right) \cdot \left\{ {{1/T_{1}}s} \right\}}}} & \quad \\{\quad{= {\left( {{\left( {{T_{1}s} + 1} \right) \cdot y_{1}} + d^{\prime} - y} \right) \cdot \left\{ {{1/T_{1}}s} \right\}}}} & \quad \\{\quad{= {\left( {{\left( {{T_{1}s} + 1} \right) \cdot y_{1}} + \left( {y - y_{2}} \right) - y} \right) \cdot \left\{ {{1/T_{1}}s} \right\}}}} & \quad \\{{\therefore\quad{T_{1}{s \cdot y_{2}}}} = {{\left( {{T_{1}s} + 1} \right) \cdot y_{1}} - y_{2}}} & \quad \\{{\therefore\quad y_{2}} = y_{1}} & \quad\end{matrix}$

Then, the control variable y is controlled on the basis of the finaldesired value y₂.

The initial desired value y₁ is directly determined as the final desiredvalue y₂, and then the manipulation variable x is determined. This makesit possible to markedly reduce phase lags of the final desired value y₂and the control variable y relative to the initial desired value y₁.

If the primary estimation value y₁′ is out of the allowable range [y⁻,y₊], then the secondary estimation value y₂′ agreeing with the lowerlimit value y⁻ or the upper limit value y₊ of the allowable range [y⁻,y₊] is determined. After that, the secondary estimation value y₂′ andthe final desired value y₂ are determined. With this arrangement, thecontrol variable y can be controlled so as to remain in the allowablerange [y⁻, y₊] even if there is the steady-state deviation d.

To explain the operation in more detail, if the primary estimation valuey₁′ is out of the allowable range [y⁻, y₊], then the secondaryestimation value y₂′ that agrees with the lower limit value y or theupper limit value y+is used, so that the transmission function from aninput to an output of the limiter 122, excluding a steady-statecomponent, is substantially “zero” (as long as the input (the primaryestimation value y₁′) is out of the allowable range [y⁻, y₊], then theoutput (the secondary estimation value y₂′) remains constant even if theinput varies). Hence, an expression (13) given below is obtained bydetermining a relationship among the secondary estimation value y₂′, thesteady-state deviation d and the control variable y. $\begin{matrix}{y = {{\left\{ {1/\left( {{T_{1}s} + 1} \right)} \right\} y_{2}^{\prime}} + {\left\{ {T_{1}{s/\left( {{T_{1}s} + 1} \right)}} \right\} d}}} & (13)\end{matrix}$

In a low frequency range (s to 0), expression (13) can be approximatedto an expression (14) given below.y≈y₂′  (14)

In other words, the control variable y substantially agrees with thesecondary estimation value y₂′ regardless of the steady-state deviationd. Thus, if the primary estimation value y₁′ is out of the allowablerange [y⁻, y₊], then the control variable y substantially agrees withthe lower limit value y or the upper limit value y₊ independently of thesteady-state deviation d.

Accordingly, the secondary estimation value y₂′ is determined such thatit remains in the allowable range [y⁻, y₊], taking the steady-statedeviation d into account, and the phase lag of the control variable yrelative to the initial desired value y₁ is restrained. This allows thecontrol variable y to be stably and accurately controlled so as tomaintain it within the allowable range [y⁻, y₊].

Referring now to FIG. 3, a control system according to a thirdembodiment of the present invention will be explained.

A block diagram of a control system 100 according to the thirdembodiment shown in FIG. 3 is obtained by assuming that the timeconstants T₁ and T₂ of the first filter 113 and the second filter 114share the same time constant T as that in the control system 100according to the first embodiment shown in FIG. 1, and combining the twofilters 113 and 114 into one filter.

The control system 100 according to the third embodiment is equippedwith a limiter 131, an inverse model arithmetic unit 132, and a filter133.

The limiter 131 and the inverse model arithmetic unit 132 share the sameconstructions as those of the limiter 111 and the inverse modelarithmetic unit 112 in the control system 100 according to the firstembodiment. The filter 133 is a primary lag filter of time constant T.

The control system 100 according to the third embodiment determines thesteady-state deviation estimation value d′ according to an expression(15) given below.d′={1/(Ts+1)}·(y−y ₂)  (15)

Referring now to FIG. 4, a control system according to a fourthembodiment of the present invention will be explained.

The block diagram of a control system 100 according to the fourthembodiment shown in FIG. 4 can be obtained by omitting the second filter114 in the control system 100 according to the first embodiment shown inFIG. 1 on the basis of the approximation of T₂ s˜0.

The control system 100 according to the fourth embodiment is equippedwith a limiter 141, an inverse model arithmetic unit 142, and a filter143.

The limiter 141 and the inverse model arithmetic unit 142 have the sameconstructions as those of the limiter 111 and the inverse modelarithmetic unit 112 in the control system 100 according to the firstembodiment. The filter 143 corresponds to the first filter 113 in thecontrol system 100 according to the first embodiment and it is a primarylag filter having a time constant T.

The control system 100 according to the fourth embodiment determines asteady-state deviation estimation value d′ according to an expression(16) given below.d′=y−{1/(Ts+1)}·y ₂  (16)

Referring now to FIG. 5, a control system according to a fifthembodiment of the present invention will be explained.

The control system 100 according to the fifth embodiment shown in FIG. 5is equipped with a limiter 151, a manipulation variable determining unit152, and a filter 153. The limiter 151, the manipulation variabledetermining unit 152, and the filter 153 correspond to the limiter 141,the inverse model arithmetic unit 142, and the filter 143, respectively,in the control system 100 of the fourth embodiment shown in FIG. 4. Inthe fourth embodiment, however, the inverse model arithmetic unit 142 isinserted as a series compensation element in a stage preceding thecontrol system 100, thereby improving the phase characteristic in theaspect of feedforward.

In the fifth embodiment, its phase characteristic has been improved bythe feedback type manipulation variable determining unit 152. Thecontrol system 100 according to the fifth embodiment controls a speed(control variable) v of a motor (controlled object) 200 by an appliedvoltage (manipulation variable) E. The following will explain thecontrol.

In the fifth embodiment, an initial desired value I₁ of a motor currentI is determined on the basis of a difference v₁−v between the motorspeed v and its initial desired value v₁ according to an expression (17)given below.I ₁ =Kvv·(v ₁ −v)  (17)

-   -   where Kvv denotes a predetermined gain.

The manipulation variable determining unit 152 determines the voltage Eto be applied to the motor 200 on the basis of a difference (=I₂−I)between the motor current I and its final desired value I₂ according toan expression (18) given below.E=G′·(Kip+Kivs)·(I ₂ I)  (18)

-   -   where G′ denotes a transmission element of a switching device        controlling the voltage E applied from a power source (not        shown) to the motor 200 in response to PWM signals, Kip and Kiv        denote a P gain and a D gain, respectively, in a PD control rule        for generating PWM signals.

The motor current I and the motor speed v based on the voltage E appliedare represented by expressions (19) and (20), respectively, given below.I={1/(R+Ls)}·(E−K _(E) v)  (19)v=(K _(T) /Js)·I  (20)

-   -   where R denotes motor resistance, L denotes motor inductance,        K_(E) denotes an induced voltage constant, K_(T) denotes a        torque constant, and J denotes a motor inertia.

In the control system 100 according to the fifth embodiment, anestimation value (steady-state deviation estimation value) d′ of acurrent control offset d generated by a counter-electromotive forceK_(E)v of the motor 200 is determined by an expression (21) given below.d′=1·I−{1/(Ts+1)}·I ₂  (21)

The control system 100 according to the fifth embodiment permits stableand accurate control so that the motor current I remains in itsallowable range [I⁻, I₊] and the motor speed v remains in its allowablerange [v⁻, v₊] even if the counter-electromotive force K_(E)v isproduced in the motor 200.

Referring now to FIG. 6, FIG. 8, and FIG. 9, a control system accordingto a sixth embodiment will be explained. A control system 100 shown inFIG. 6 controls an angle (control variable) y=(θ, φ) of the motor 200(controlled object) attached to a joint of an arm 202 of a manipulatorshown in FIG. 8. Thus, the position (height h or the like from an object220) of a hand 204 attached to a distal end of the arm 202 iscontrolled.

The control system 100 according to the sixth embodiment shown in FIG. 6is equipped with a limiter 161, a manipulation variable determining unit162, and a filter 163.

If a primary estimation value y₁′=(θ₁′, φ₁′) of a joint angle (=motorangle) y=(θ, Φ) of the arm 202 of the manipulator shown in FIG. 8 iswithin the allowable range shown in FIG. 9, then the limiter 161determines a secondary estimation value y₂′=(θ₂′, φ₂′) that agrees withthe primary estimation value y₁″=(θ₁′, Φ₁′). Meanwhile, if the primaryestimation value y₁′=(θ₁′, φ₁′) is out of the allowable range shown inFIG. 9, then the limiter 161 determines a secondary estimation valuey₂′=(θ₂′, φ₂′) that agrees with a boundary value of the allowable rangethat is closest to the primary estimation value y₁′=(θ₁′, φ₁′) (at whicha distance norm is minimum).

The manipulation variable determining unit 162 outputs a motor current(manipulation variable) x=(i, j) on the basis of an input differencebetween a final desired value y₂=(θ₂, φ₂) and the control variable y=(θ,φ) according to an expression (22).x=(Kpp+Kpvs)(y ₂ −y)  (22)

-   -   where Kpp and Kpv denote a P gain and a D gain, respectively, of        a PD control rule to which the manipulation variable determining        unit 162 conforms.

The filter 163 is represented in the form of a 2×2 diagonal matrix Faccording to an expression (23) given below.F=diag[1/(Ts+1), 1/(Ts+1)]  (23)

The control system 100 according to the sixth embodiment permits stableand accurate control to be accomplished so that the joint angle γ=(θ, φ)remains in its allowable range (refer to FIG. 9) even when thesteady-state deviation d takes place in the motor 200. Moreover, thecontrol can be carried out such that a hand 204 attached to a distal endof the arm 202 remains in its allowable range.

The manipulation variable x and the control variable y or the like maybe represented in the form of n-dimensional vectors (n≧3). At this time,the filter is represented as an n×n diagonal matrix having a lag elementas a diagonal component (refer to expression (19)). However, thediagonal component may be “1” for a control variable component on whichthe steady-state deviation d may be ignored.

By mapping f represented as the n×n diagonal matrix, points P₁ to P₄ inan n-dimensional primary estimation value space conceptually shown inFIG. 10 are mapped in an n-dimensional secondary estimation value space.Mappings f (P₂)=Q₂ and f (P₃)=Q₃ of points P₂ and P₃ located within anallowable range C in the primary estimation value space agree withpoints P₂ and P₃, respectively. Mappings f (P₁)=Q₁ and f (P₄)=Q₄ ofpoints P₁ and P₄ located out of the allowable range C in the primaryestimation value space are mapped at boundary values of the allowablerange C that are close to points P₁ and P₄, respectively. The mappingfunction f may be a smooth function, that is, a function in which graddoes not suddenly change. This will make time-dependent changes of thecontrol variable y also smooth.

The control systems 100 in the aforesaid embodiments may be discretizedby forward difference, backward difference, bilinear transformation,etc.

For example, FIG. 11 is a block diagram of a control system 100 obtainedby discretizing the control system 100 according to the secondembodiment shown in FIG. 2 by a forward difference.

The block diagram of the control system 100 shown in FIG. 11 is obtainedby approximating the transmission element Gm⁻¹ and G to “1” and thenperforming discretization by forward difference in the control system100 in the second embodiment shown in FIG. 2. In this case, ΔT is acontrol cycle. An output of a unit of a transmission element 1/zrepresents a previous value of a unit input (the unit input determinedbefore time ΔT) constituted of the initial desired value y₁ and thefinal desired value y₂. The time constant T is set to a value of ΔT ormore.

In any one of the aforesaid embodiments, the transmission elements ofthe filters may be represented more generally.

For instance, in the control system 100 according to the firstembodiment shown in FIG. 1, the transmission element F₁ of the firstfilter 113 may be represented as a general form according to anexpression (24) given below by B₁ (s) and C₁ (s) of a lower order thanB₁ (s). Similarly, the transmission element F₂ of the second filter 114may be represented as a general form according to an expression (25)given below by B₂ (s) and C₂ (s) of the same order as or a lower orderthan C₁ (s).F ₁ =C ₁(s)/B ₁(s)  (24)F ₂ =C ₂(s)/B ₂(s)  (25)

The control unit 100 may be provided with an initial desired valuedetermining unit (not shown) for determining the initial desired valuey₁ according to an expression (26) given below on the basis of an inputinitial manipulation variable x₁ determined manually or by anothercontrol system (not shown). The transmission element Gm of the initialdesired value determining unit corresponds to an inverse function of thetransmission element Gm⁻¹, such as the inverse model arithmetic unit112.y ₁ =Gm·x ₁  (26)

1. A control system for controlling a control variable y of a controlledobject through a manipulation variable x, comprising: a steady-statedeviation estimating means for estimating a steady-state deviation d ina controlled object as a steady-state deviation estimation value d′based on the control variable y and a final desired value y₂; a primaryestimating means for estimating the control variable y of the controlledobject according to an initial desired value y₁ as a primary estimationvalue y₁′ based on at least the initial desired value y₁ and thesteady-state deviation estimation value d′; a desired value determiningmeans for determining a final desired value y₂ agreeing with the initialdesired value y₁ if the primary estimation value y₁′ is within anallowable range, while determining the final desired value y₂ based onat least a boundary value of the allowable range if the primaryestimation value y₁′ is out of the allowable range; and a manipulationvariable determining means for determining a manipulation variable xaccording to the final desired value y₂.
 2. The control system accordingto claim 1, wherein the steady-state deviation estimating meansestimates, as the steady-state deviation estimation value d′, adifference between the control variable y and a value obtained bypassing the final desired value y₂ through a low-pass filter or adelaying means.
 3. The control system according to claim 1, wherein thesteady-state deviation estimating means estimates, as the steady-statedeviation estimation value d′, a difference between a value obtained bypassing the control variable y through a low-pass filter or the delayingmeans and a value obtained by passing the final desired value y₂ througha low-pass filter or a delaying means.
 4. The control system accordingto claim 1, wherein the steady-state deviation estimating meansestimates, as the steady-state deviation estimation value d′, a valueobtained by passing a difference between the control variable y and thefinal desired value y₂ through a low-pass filter or a delaying means. 5.The control system according to claim 1, wherein the primary estimatingmeans estimates a sum of the initial desired value y₁ and thesteady-state deviation estimation value d′ or a value obtained bypassing the sum y₁+d′ through a low-pass filter or a delaying means asthe primary estimation value y₁′.
 6. The control system according toclaim 1, further comprising a secondary estimating means for directlyestimating the primary estimation value y₁′ as a secondary estimationvalue y₂′ if the primary estimation value y₁′ is within the allowablerange, while estimating a value within the allowable range as thesecondary estimation value y₂′ if the primary estimation value y₁′ isout of the allowable range, and the desired value determining meansdetermines the final desired value y₂ based on the secondary estimationvalue y₂′ and the steady-state deviation estimation value d′.
 7. Thecontrol system according to claim 6, wherein, based on the primaryestimation value y₁′, the secondary estimating means determines thesecondary estimation value y₂′ by a continuous or smooth mapping fromthe primary estimation value y₁′ to the secondary estimation value y₂′.8. The control system according to claim 6, wherein the desired valuedetermining means subtracts the steady-state deviation estimation valued′ from the secondary estimation value y₂′ to determine the finaldesired value y₂.
 9. The control system according to claim 6, whereinthe desired value determining means determines the final desired valuey₂ based on a difference between the control variable y and thesecondary estimation value y₂′ or a difference between the secondaryestimation value y₂′ and a value obtained by passing the controlvariable y through a low-pass filter or a delaying means according to acontrol rule for converging the difference to zero.
 10. The controlsystem according to claim 9, wherein the desired value determining meansdetermines the final desired value y₂ by passing a difference betweenthe control variable y and the secondary estimation value y₂′ or adifference between a value obtained by passing the control variable ythrough the low-pass filter or the delaying means and the secondaryestimation value y₂′ through a transmission element having at leastintegration.
 11. The control system according to claim 1, wherein themanipulation variable determining means has a transmission function Gm⁻¹that satisfies a relationship of Gm⁻¹·G≈1 between itself and atransmission function G of a controlled object.